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Journal of Russian Laser Research

Interaction Dynamics of the External and Internal Degrees of Freedom of an Atom in the Resonant Field of a Standing Light Wave

V. Yu. Sirotkin, Sergei V Prants

Published Nov 1, 2000• 2 citations
Publisher
DOI
10.1023/a:1009540612688

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The nonlinear dynamical effects of synchronization and bifurcations of Rabi oscillations and oscillations of the center of mass of an atom moving in the field of a standing light wave are theoretically and numerically examined. After completion of a transient process, synchronized oscillations, stable with respect to small noise, are established both upon ballistic motion of the atom and upon its oscillations in the optical potential well. The bifurcations of limit cycle generation with different periods (tripling of the period is most pronounced) and the passage to a chaotic strange attractor through an intermittency are obtained.

Journal of Experimental and Theoretical Physics Letters•Aug 1, 2004•3 citations
Strong coupling of the internal and external degrees of freedom of a cold atom to each other and to the spatially periodic field of the standing light wave in a high-finesse cavity is responsible for the dynamic instability of the atomic center-of-mass motion. Due to a weak interaction of the internal nonlinear resonances in the standard model of cavity QED, a stochastic layer appears, whose width in the semiclassical approximation is estimated in terms of the main parameters of the system: atomic recoil frequency, mean number of excitations, and detuning from the resonance. As a result, the atomic motion in the absolutely regular potential has the fractal character, with long Lévy flights alternating with small chaotic oscillations in potential wells.
Starting from the Jaynes-Cummings (J-C) model describing interaction of a trapped ion with a standing-wave laser field, we derive the interaction Hamiltonian on the nonlinear J-C model of the trapped ion excitated resonantly with 1-quantum vibrational mode. After solving the time-dependent states of this model,the entropy evolution of the ion are investigated numerically related with Lamb-Dick parameter,the position of the ion in the standing-wave laser field and the initial number of phonon. It is shown that the entropy evolution exhibit nonperiodicity vibration. With the increasing of the parameter, it will increase the frequency of the vibration,therefore the less time of disentanglement between the internal and external degrees of freedom of a trapped ion. When moving the ion from the node of the standing-wave laser to the antinode,the frequency of the vibration becomes less,the longer time of the disentanglement between the internal and external degrees of freedom. With the more initial number of phonon , the entropy evolution of the ion is similar to the field entropy evolution of Jaynes-Cummings model, and the vibration frequency become less gradually.
The nonlinear dynamical effects of synchronization and bifurcations of Rabi oscillations and oscillations of the center of mass of an atom moving in the field of a standing light wave are theoretically and numerically examined. After completion of a transient process, synchronized oscillations, stable with respect to small noise, are established both upon ballistic motion of the atom and upon its oscillations in the optical potential well. The bifurcations of limit cycle generation with different periods (tripling of the period is most pronounced) and the passage to a chaotic strange attractor through an intermittency are obtained.